A note on the Aitkin-Rubin approach to hypothesis testing in mixture models

B. G. Quinn; G. J. McLachlan; N. L. Hjort

A note on the Aitkin-Rubin approach to hypothesis testing in mixture models

B. G. Quinn, G. J. McLachlan, N. L. Hjort

Research output: Contribution to journal › Article › peer-review

Abstract

In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.

Original language	English
Pages (from-to)	311-314
Number of pages	4
Journal	Journal of the Royal Statistical Society. Series B: Statistical Methodology
Volume	49
Issue number	3
Publication status	Published - 1987
Externally published	Yes

Keywords

mixture model
number of components
prior distribution
likelihood ratio test

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Cite this

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title = "A note on the Aitkin-Rubin approach to hypothesis testing in mixture models",

abstract = "In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.",

keywords = "mixture model, number of components, prior distribution, likelihood ratio test",

author = "Quinn, {B. G.} and McLachlan, {G. J.} and Hjort, {N. L.}",

year = "1987",

language = "English",

volume = "49",

pages = "311--314",

journal = "Journal of the Royal Statistical Society. Series B: Statistical Methodology",

issn = "1369-7412",

publisher = "Wiley-Blackwell, Wiley",

number = "3",

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TY - JOUR

T1 - A note on the Aitkin-Rubin approach to hypothesis testing in mixture models

AU - Quinn, B. G.

AU - McLachlan, G. J.

AU - Hjort, N. L.

PY - 1987

Y1 - 1987

N2 - In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.

AB - In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.

KW - mixture model

KW - number of components

KW - prior distribution

KW - likelihood ratio test

M3 - Article

VL - 49

SP - 311

EP - 314

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

SN - 1369-7412

IS - 3

ER -

A note on the Aitkin-Rubin approach to hypothesis testing in mixture models

Abstract

Keywords

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